Atom-chip-based generation of entanglement for quantum metrology

Abstract

Atom chips provide a versatile quantum laboratory for experiments with ultracold atomic gases. They have been used in diverse experiments involving low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. However, a severe limitation of atom chips is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations, quantum information processing and quantum metrology. Here we report the experimental generation of multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential. We use this technique to generate spin-squeezed states of a two-component Bose-Einstein condensate; such states are a useful resource for quantum metrology. The observed reduction in spin noise of -3.7 +/- 0.4 dB, combined with the spin coherence, implies four-partite entanglement between the condensate atoms; this could be used to improve an interferometric measurement by -2.5 +/- 0.6 dB over the standard quantum limit. Our data show good agreement with a dynamical multi-mode simulation and allow us to reconstruct the Wigner function of the spin-squeezed condensate. The techniques reported here could be directly applied to chip-based atomic clocks, currently under development.

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

“…Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1][2][3][4][5][6][7][8][9][10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11,12], and very recently in large atomic ensembles [13][14][15].…”

“…Entanglement can be verified in a variety of ways, with one of the strictest criteria being a negative-valued Wigner function [16,17], that necessarily implies that the entangled state has a non-Gaussian wavefunction. To date, the metrologically useful spin-squeezed states [1][2][3][4][5][6][7][8][9][10] have been produced in large ensembles. These states have Gaussian spin distributions and therefore can largely be modeled as systems with a classical source of spin noise, where quantum mechanics enters only to set the amount of Gaussian noise.…”

Quantum Fisher information and spin squeezing in one-axis twisting model

“…Equation (1) shows that a quantum state with the APEP-enhancing must be entangled. Besides entangled states, it has been theoretically and experimentally demonstrated that spin squeezed states (SSSs) can also be used to improve the accuracy of estimation [8,9,10,11,12,13,14,15,16,17,18,19]. The concept of SSSs was first established by Kitagawa and Ueda [9].…”

Microscopic theory of a phase transition in a critical region: Bose–Einstein condensation in an interacting gas

“…It becomes possible due to the newly developed methods of (a) the nonpolynomial averages and contraction superoperators [15,16], (b) the partial difference (recurrence) equations [17][18][19] (a discrete analog of the partial differential equations) for superoperators, and (c) a characteristic function and cumulant analysis for a joint distribution of the noncommutative observables. They allow us to take into account (I) the constraints in a many-body Hilbert space, which are the integrals of motion prescribed by a broken symmetry in virtue of a Noether's theorem, and constraintcutoff mechanism, responsible for the very existence of a phase transition and its nonanalytical features, [4,20,21] (II) an insufficiency of a grand-canonical-ensemble approximation, which is incorrect in the critical region [2,8] because of averaging over the systems with different numbers of particles, both below and above the critical point, i.e., over the condensed and noncondensed systems at the same time, that implies an error on the order of 100% for any critical function, (III) a necessity to solve the problem for a finite system with a mesoscopic (i.e., large, but finite) number of particles N in order to calculate correctly an anomalously large contribution of the lowest energy levels to the critical fluctuations and to avoid the infrared divergences of the standard thermodynamic-limit approach [5][6][7][8][9][10][11] as well as to resolve a fine structure of the λ-point, (IV) a fact that in the critical region the Dyson-type closed equations do not exist for true Green's functions, but do exist for the partial 1-and 2-contraction superoperators, which reproduce themselves under a contraction.The problem of the critical region and mesoscopic effects is directly related to numerous modern experiments and numerical studies on the BEC of a trapped gas (including BEC on a chip), where N ∼ 10 2 − 10 7 , (see, for example, [22][23][24][25][26][27][28][29][30][31][32][33]) and superfluidit...…”

“…The problem of the critical region and mesoscopic effects is directly related to numerous modern experiments and numerical studies on the BEC of a trapped gas (including BEC on a chip), where N ∼ 10 2 − 10 7 , (see, for example, [22][23][24][25][26][27][28][29][30][31][32][33]) and superfluidity of 4 He in nanodroplets (N ∼ 10 8 − 10 11 ) [34] and porous glasses [35].…”